Buckling and delamination of sandwich structure systems

Research Team

• Professor Ahmer Wadee: Imperial College London
• Dr Stylianos Yiatros: Cyprus University of Technology (former PhD student)
• Professor Giles Hunt: University of Bath
• Dr Avril Blackmore: University College London
• Professor Luis Simões da Silva: University of Coimbra, Portugal

Background

Sandwich construction is a mass efficient structural form used extensively in astronautic, aeronautic and marine applications. Sandwich panels are used as members for general loading situations: bending, shear and axial loading. In axial compression, however, there are serious structural integrity issues precisely because of their inherent efficiency; their susceptibility to highly unstable interactive buckling phenomena in practical situations is widely accepted [1].  Research conducted by the Nonlinear Mechanics group initially at Imperial College London, then at the University of Bath and again at Imperial has led to the development of a sequence of models that account for the severe interaction between overall (Euler-type) and local modes of buckling that leads to highly unstable post-buckling [2,3]. Moreover, the practically important issue of buckle pattern localization [4] has been addressed such that the models can be compared favourably with physical experiments [5] in a variety of cases. These models have identified the problems with using orthotropic core materials [6], having pre-existing defects in terms of lack of straightness in the face plates and face-core delamination [7-9]. Other effects from panel asymmetry [10], different bending models [11] , beam-columns [12] and functionally graded cores [13] have been addressed. These effects do not significantly affect the classically obtained critical load from small deflection theory, but they can have severe implications on the post-critical load-carrying capacity of the sandwich structure concerned. Moreover, the nonlinear effects can seriously question the practical value of linear analysis for these cases, as it would give unsafe estimates of the true load capacity of the structural component and therefore significant factors of safety would need to be applied in relevant design rules.

Context and Methodology

The initial work on the interactive buckling in the sandwich panel began in the mid 1980s at Imperial where Dr Giles Hunt (GWH) and Luis Simões da Silva (LSdS) developed a multiple degree-of-freedom model accounting for periodic buckling using the Rayleigh-Ritz method. In parallel, however, progress was being made in developing methods for analysing the conditions where buckle pattern localization could occur particularly in the archetypal model of the strut on an elastic foundation: a classic model for a compression sandwich structure. In the mid 1990s, therefore, work by GWH (now at the University of Bath) and Ahmer Wadee (MAW) began on applying the analytical and numerical modelling techniques developed for localized buckling problems to convert the basically qualitative models of sandwich panels into quantitative ones with the success described above. The research has continued once again at Imperial with further model developments from MAW in collaboration with Dr Avril Blackmore, LSdS and (now Dr) Stylianos Yiatros.

The numerical solution involves employing shooting techniques using an implicit Gauss-Legendre Runge-Kutta initial value solver, in conjunction with the boundary value solving and numerical continuation package, AUTO, coordinated by Professor Eusebius Doedel at Concordia University, Montreal, Canada. The software is freely available and the latest release may be obtained from sourceforge.

Seminars and Conference Presentations

• December 2012
  Glasgow, UK. 6th International Conference on Coupled Instabilities in Metal Structures (CIMS 2012). Delivered by Stylianos Yiatros.
• June 2012
  Notre Dame, USA. ASCE/EMI Conference 2012 (EMI/PMC 2012). Delivered by Stylianos Yiatros.
• September 2010
  Cape Town, South Africa. Fourth International Conference on Structural Engineering, Mechanics and Computation (SEMC 2010).
• July 2010
  University of the Witwatersrand, Department of Civil and Environmental Engineering, Johannesburg, South Africa. Research Seminar.
• June 2009
  1) Bath Institute for Complex Systems. Symposium: Reflections in Nonlinear Mechanics. (Invited)
  2) Blacksburg, USA, Joint ASCE-ASME-SES Conference. (Invited)
• May 2006
  University of Bath, Centre for Nonlinear Mechanics. Brooke Session.
• April 2003
  University of Leicester, East Midlands Mathematical Physics Seminar. Research Seminar.
• February 2002
  University of Bath, Centre for Nonlinear Mechanics. Brooke Session.
• September 2000
  Lisbon, Portugal. Third International Conference on Coupled Instabilities in Metal Structures (CIMS'2000).
• February 2000
  University College London, Centre for Nonlinear Dynamics and its Applications. Dynamics Seminar.
• February 1998
  University of Sydney, Australia. Australasian Conference on Structural Optimization (ACSO'98).
• January 1998
  University of Bath, Centre for Nonlinear Mechanics. Brooke Session.
• June 1997
  University of Exeter, School of Engineering. Research Seminar.
• December 1996
  University of Bristol, Department of Engineering Mathematics. Nonlinear Workshop.

References

1. Hunt, G. W. 1986. Hidden (a)symmetries of elastic and plastic bifurcation. Appl. Mech. Rev. 39:1165-1186.
2. Hunt, G. W., Da Silva, L. S. and Manzocchi, G. M. E. 1988. Interactive buckling in sandwich structures. Proc. R. Soc. A, 417:155-177.
3. Hunt, G. W. and Da Silva, L. S. 1990. Interactive bending behaviour of sandwich beams. J. Appl. Mech. - Trans ASME, 57:189-196.
4. Hunt, G. W. and Wadee, M. A., 1998. Localization and mode interaction in sandwich structures. Proc. R. Soc. A, 454:1197-1216.
5. Wadee, M. A. and Hunt, G. W., 1998. Interactively induced localized buckling in sandwich structures with core orthotropy. J. Appl. Mech. - Trans. ASME, 65:523-528.
6. Wadee, M. A., 1999. Experimental evaluation of interactive buckle localization in compression sandwich panels. J. Sandw. Struct. Mater., 1:230-254.
7. Wadee, M. A., 2000. Effects of periodic and localized imperfections on struts on nonlinear foundations and compression sandwich panels. Int. J. Solids Struct., 37:1191-1209.
8. Wadee, M. A. and Blackmore, A., 2001. Delamination from localized instabilities in compression sandwich panels. J. Mech. Phys. Solids, 49:12 81-1299.
9. Wadee, M. A., 2002. Localized buckling in sandwich struts with pre-existing delaminations and geometrical imperfection s. J. Mech. Phys. Solids, 50:1767-1787.
10. Wadee, M. A. and Simões da Silva, L. A. P., 2005. Asymmetric secondary buckling in monosymmetric sandwich struts. J. Appl. Mech.-Trans. ASME , 72:683-690.
11. Wadee M. A., Yiatros, S. and Theofanous, M., 2010. Comparative studies of localized buckling in sandwich struts with different core bending models. Int J. Non-Linear Mech., 45:111-120.
12. Yiatros, S. and Wadee, M. A., 2011. Interactive buckling in sandwich beam-columns. IMA J. Appl. Math., 76:146-168.
13. Yiatros, S., Wadee, M. A. and Völlmecke, C. 2013. Modelling of interactive buckling in sandwich struts with functionally graded cores. J. Eng. Mech. - ASCE, 139:952-960. Special issue.

 Doctoral Theses

• M . Ahmer Wadee. Localized buckling in sandwich structures, PhD thesis, University of Bath, 1998.
• Stylianos Yiatros. Mode interaction and localization in sandwich struts and beam-columns, PhD thesis, Imperial College of Science, Technology and Medicine, University of London, 2010.